# [EM] Better cardinal methods?

Forest Simmons forest.simmons21 at gmail.com
Tue Oct 5 16:51:07 PDT 2021

```Richard,

Thanks for stimulating my imagination!

Forest

El mar., 5 de oct. de 2021 4:38 p. m., Richard Lung <voting at ukscientists.com>
escribió:

>
>
> Dear All,
>
>  But Elections are a statistic -- a sum of contingent choices. Votes are
> not in a logical relation to each other, such that there is some
> determinable right answer to who should be elected. Axiomatic deduction of
> a deterministic result is the reason why the Impossibility theorem is
> impossible -- it is a misconception of the nature of elections.
>
> We can make probabilistic determinations of electing candidates, ranging
> from practically certain to completely indecisive. The most representative
> results depend on most representatively averaging the preference data. This
> avoids the usual social choice theory objections, that assume elections are
> analytic rather than synthetic.
>
> Regards,
> Richard Lung.
>
>
>
> On 5 Oct 2021, at 10:46 pm, Kristofer Munsterhjelm <km_elmet at t-online.de>
> wrote:
>
> > On 05.10.2021 04:54, Andy Jennings wrote:
> > Forest,
> >
> > Thanks for your thoughts.
> >
> > I agree that there are many good ways to get cardinal information from
> > voters on a valid interval scale, assuming that we don't try to compare
> > intervals between voters. It seems that the cardinal information must be
> > meaningful and it's a shame to throw it away (though I agree that the
> > method should be invariant to affine transformations).
> >
> > Speaking of lottery methods, it's interesting that there is so much
> > reluctance (including my gut reaction) to actually recommend a
> > lottery-based method for use in real political elections. We want our
> > elections to be deterministic, not influenced by chance in any way. But
> > certainly there is chance in the process. Weather can influence turnout,
> > as can traffic. There may be some voters that actually flip a coin in
> > the voting booth. Cosmic rays have affected vote counts in the past
> > (https://youtu.be/AaZ_RSt0KP8?t=44 <https://youtu.be/AaZ_RSt0KP8?t=44>).
> > Websites like FiveThirtyEight report on the whole election season with
> > probabilities. And sitting there watching outcomes on election night can
> > definitely feel like games-of-chance-and-skill like the Olympics.
> >
> > So maybe we should just embrace it and try to convince people to use
> > lottery methods.
>
> If lotteries are on the table, then perhaps we should just dissolve the
> electoral problem and go right to sortition. It certainly has appealing
> corruption resistance properties :-)
>
> But the problem of lotteries, I think, is that there's too much left to
> chance. While every election leaves something to chance (as you've
> correctly pointed out), it's not too much to destabilize the process. On
> the other hand, if you have the simple random favorite lottery and 10%
> of the voters vote for a dictator, then you have 10% chance of getting a
> dictatorship.
>
> One way of considering single-winner methods, I think, is that they try
> to find the best outcome under the constraint of zero entropy.
> Proportional representation methods might also need to compromise to
> satisfy their seat limits. Perhaps it would be possible to create a
> tunable entropy method where we set a maximum allowed entropy (or
> variance), and it attempts to find the best outcome lottery subject to
> this constraint. Such a constraint would help with the reluctance, I
> think, as long as the threshold is set sufficiently low that there's no
> chance of extreme upsets (like a dictator winning).
>
> > Even if we trust the math that generates the lottery, maybe we just
> > can't bring ourselves to believe that the final draw will not be rigged.
> > I'm sure there are cryptographic methods for securely generating a
> > random number between 0 and 1, but will the public trust them?
>
> that goes like this:
>
> Somehow pick a number of participants (they may be the whole electorate
> or randomly chosen members of the public, or the representatives of the
> previous term).
>
> Each participant creates a sufficiently long random secret string and
> publishes its cryptographic hash.
>
> The participants (or the election officials) publish these hashes.
>
> Once they're all published, each participant reveals his random string.
> If they match their respective hashes, the strings are combined, and the
> result is used as a seed for a CSPRNG.
>
> This protocol works by forcing the participants to commit to their input
> strings before they have any knowledge of the other strings. Thus they
> can't adapt the inputs to fix a particular output.
>
> Suppose there's a conspiracy to fix the output by bribing or coercing
> the participants into selecting predetermined random strings. Then even
> if a single member defects from the conspiracy, the chaotic nature of
> the secure hash function makes the attack fail. If the combination
> function is secure (e.g. a secure hash), then a conspiracy would in any
> case have to use brute force to find a suitable set of strings. The
> difficulty of this brute-forcing would depend on the entropy - e.g.
> packing a majority of a sortition assembly of 100 would be prohibitive,
> but changing the outcome of an election lottery with a few candidates
> would be easier.
>
> > Is the NIST randomness beacon trustworthy?
> >
> > In a small enough election, you could agree to use randomness from the
> > next block mined on the bitcoin blockchain, but that runs into problems
> > at the scale of a national election.
>
> There have been proposals to use public data as entropy sources, e.g.
> this one for financial data:
> https://www.usenix.org/legacy/event/evtwote10/tech/full_papers/Clark.pdf
>
> If multiple countries were to provide signed public randomness beacons,
> they could be used as part of the protocol above; every country would
> have to be collaborating to force the output. Number stations would
> *almost* work, except they aren't signed.
>
> -km
> ----
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>
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